The International Business Times has a terrific “user guide” piece about the Kindle Fire. From the article:
Maximize Battery Life
There are a number of tricks you can use to maximize your Kindle Fire’s battery life. First, each time you are finished using your Kindle, be sure to put it to sleep by tapping the power button on the bottom of the Kindle. Another trick to maximize your Kindle Fire’s battery life is to turn off WiFi when you do not need to be connected to the Internet. You can also lower the brightness of the Kindle Fire screen to preserve power. Lastly, you can set your Kindle screen to lock automatically (thereby setting it in sleep mode), which will also save power energy.
Close Running Applications
Applications that are running in the background will hurt your battery life and also might cause your Kindle Fire to slow down. To check what applications are running in the background of your Kindle Fire, return to the settings menu. Select “more” and then “applications.” Once you are in the “applications” section of the settings, you will be able to see all the applications that are running in the background of your Kindle Fire. Select an application that you wish to close and select “force stop.” The application will now be closed and you may notice your Kindle Fire is running faster than before.